3) Una compañía llantera requiere construir en un lote de 50 por 100 m la barda de un terreno rectangular de 550 m² de superficie. El lado que da al norte quedará sin barda porque será utilizado como entrada al negocio.

¿Qué dimensiones deberá tener el terreno para que la suma de la longitud de la barda sea la mínima?

To minimize the sum of the fence length, find the dimensions of the rectangular lot minimizing fencing, considering an open side. Differentiate the perimeter to find the critical point for optimal dimensions.

Explanation:

To minimize the sum of the length of the fence, we need to find the dimensions of the rectangular lot that minimize the fencing needed. The area of the rectangle is 550 m², and since one side is left open for the entrance, the perimeter to be minimized is 50m + 2x, where x is the length of the side opposite the open side. By differentiating the perimeter (P) with respect to x and setting it to zero to find the critical point, we can determine the dimensions needed to minimize the fencing.

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